Announcement of the Study Guide Subsurface Image and Parameter Estimation in Seismic Exploration

Abstract

In this book, we will delve into the mathematical world of seismic exploration, considering methods for constructing subsurface images from the standpoint of the geometrical theory of imaging, as well as methods for estimating geological-medium parameters by solving inverse kinematic and dynamic problems. Using Fermat’s principle, formulas for traveltime fields are derived. These formulas will help us gain a deeper understanding of the essence of the Common Depth Point (CDP) method and of ways to determine velocity from seismic data. Let us consider how interference can be suppressed by focusing over large apertures. This will allow us to better understand how interference-suppression methods work. We will discuss how velocity can be determined from seismic data. The main factor affecting the relationship between stacking velocity and velocity in the medium is the horizontal variation of velocity in the medium. We will derive the Lynn equation, which will help us determine velocities while taking this factor into account. Let us talk about diffraction. Large-aperture focusing methods that take the curvature of the reflecting boundary into account make it possible, when its curvature tends to infinity, to effectively isolate diffraction phenomena. Examples of their detection are presented on synthetic and real time sections from surveys in the Laptev Sea (Khatanga Bay) and the Gulf of Mexico. We will discuss the main tasks of seismic-data interpretation: tracking reflecting horizons, matching times at profile intersections, data smoothing, depth calculation and mapping, and assessment of the accuracy of structural mapping. The book proposes a method for color visualization of seismic images based on the wave nature of seismic waves. The resulting color images may become a valuable tool in hydrocarbon exploration. Methods of seismic-stratigraphic modeling and stacking are considered in detail. These methods are intended for interference suppression and can provide kinematic information at any times of seismic observations for inverse problems, including reflected-wave tomography. The physical foundations of migration, demigration, integral modeling, and ray modeling are considered, together with algorithms for the software implementation of these methods. The inverse dynamic problem of determining the parameters of a viscoelastic medium from the wavefield is considered. Unlike full-waveform inversion (FWI), which is based on iterative model fitting and repeated solution of the forward problem, the proposed approach is based on solving an inverse coefficient problem for the wave equation. Two methods for determining the elastic parameter and the stress relaxation time from the VSP wavefield are considered. The wave equations are written in a unified form for the Maxwell model and the standard linear solid. Based on analysis of the frequency characteristics of seismic data, a method is proposed for improving the vertical resolution of seismic records. This method has found application in the problem of determining the effective thickness of thin beds. An innovative algorithm for the automated determination of oil-and-gas accumulation areas and the structural traps contained within them is offered to petroleum specialists. Results of applying the algorithm using S. G. Neruchev’s methodology for estimating hydrocarbon resources are presented for fields in the Lower Neocomian deposits of the Tanama Structural Terrace of the Yenisei-Khatanga Regional Trough. This book is intended for readers who wish to deepen their knowledge of the mathematical aspects of the seismic method. It will be useful to specialists engaged in seismic-data processing and interpretation in industrial organizations, as well as to researchers. In addition, the book will be of interest to senior undergraduate and graduate students studying applied mathematics, geophysics, and geophysical methods of mineral exploration. It can also be used in preparing specialized courses in these fields.Related publications:Inverse Dynamic Problem in a Viscoelastic Medium — DOI: 10.5281/zenodo.21723472Author’s Archive of Research Materials Published on the CALAMEO Digital Publishing Platform — DOI: 10.5281/zenodo.21978229